- Series
- Math Physics Seminar
- Time
- Wednesday, March 13, 2024 - 1:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Shivan Mittal – Department of Physics, The University of Texas at Austin – shivan@utexas.edu
- Organizer
- Federico Bonetto

**Please Note:** Available online at: https://gatech.zoom.us/j/98258240051

Consider the following question of interest to cryptographers: A message is encoded in a binary string of length n. Consider a set of scrambling operations S (a proper subset of permutations on n bits). If a scrambling operation is applied uniformly at random from S at each step, then after how many steps will the composition of scrambling operations look like a random permutation on all the bits? This question asks for the convergence time for a random walk on the permutation group. Replace the binary string with a quantum state and scrambling operations in S with Haar random quantum channels on two bits (qudits) at a time. Broadly speaking, we study the following question: If a scrambling operation is applied uniformly at random from S at each step, then after how many steps will the composition of scrambling operations (quantum channels) look like a Haar random channel on all qudits? This questionÂ asks about the convergence time for a random walk on the unitary group. Various protocols in quantum computing require Haar random channels, which motivates us to understand the number of operations one would require to approximately implement that channel.